few_shots: Example:
Problem/activity:
Narrative
The purpose of this activity is for students to create composite shapes and compose new shapes from composite shapes. For example, students may find that a rectangular prism can be made from four triangular prisms or from eight smaller cubes. Students then discover that they can combine two of the composed rectangular prisms to make a new rectangular prism.
Required Materials
Materials to Gather
Geoblocks
Launch
Groups of 4
Give each group geoblocks.
Display a large cube.
“This cube can be built from other shapes. See how many ways you can build a cube using other shapes.”
3 minutes: partner work time
Share responses.
Activity
“Choose a different shape. Try to find smaller shapes you can use to build that shape.”
5 minutes: partner work time
Student Response
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click here to register or sign in
for free access to Student Response.
Activity Synthesis
Display a cube and a composite cube—for example, a cube composed of four small cubes and one rectangular prism.
Demonstrate putting the shapes together.
“What new shape did I make with the cube and the cube I made?”
“Put your shapes together to make a rectangular prism.”
Display a rectangular prism and two triangular prisms.
“Find these shapes. Put them together. What new shape can you make?” (a cube, a rectangular block)


Mathematical concept/skill options: 
A. Reason with shapes and their attributes.
B. Understand similarity in terms of similarity transformations.
C. Use coordinates to prove simple geometric theorems algebraically.
D. Translate between the geometric description and the equation for a conic section.
E. Understand congruence and similarity using physical models, transparencies, or geometry software.
F. Analyze, compare, create, and compose shapes.
G. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
H. Understand congruence in terms of rigid motions.
I. Classify two-dimensional figures into categories based on their properties.
J. Draw, construct, and describe geometrical figures and describe the relationships between them.
K. Explain volume formulas and use them to solve problems.
L. Prove theorems involving similarity.
M. Prove geometric theorems.
N. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
O. Define trigonometric ratios and solve problems involving right triangles.
P. Apply trigonometry to general triangles.
Q. Visualize relationships between two-dimensional and three-dimensional objects.
R. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
S. Make geometric constructions.
T. Apply geometric concepts in modeling situations.
U. Solve real-world and mathematical problems involving area, surface area, and volume.
V. Graph points on the coordinate plane to solve real-world and mathematical problems.
W. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
X. Understand and apply theorems about circles.
Y. Understand and apply the Pythagorean Theorem.
Z. Experiment with transformations in the plane.
AA. Find arc lengths and areas of sectors of circles.


Thought: This activity asks students to reason how shapes can combine to make other shapes.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_lesson_009431

1
options: Represent and solve equations and inequalities graphically.

Understand solving equations as a process of reasoning and explain the reasoning.

Reason about and solve one-variable equations and inequalities.

Generate and analyze patterns.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Understand the relationship between zeros and factors of polynomials.

Use properties of operations to generate equivalent expressions.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Interpret the structure of expressions.

Create equations that describe numbers or relationships

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving addition and subtraction.

Work with equal groups of objects to gain foundations for multiplication.

Represent and analyze quantitative relationships between dependent and independent variables.

Analyze patterns and relationships.

Multiply and divide within 100.

Write and interpret numerical expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Perform arithmetic operations on polynomials.

Add and subtract within 20.

Work with radicals and integer exponents.

Represent and solve problems involving multiplication and division.

Gain familiarity with factors and multiples.

Use polynomial identities to solve problems.

Understand and apply properties of operations and the relationship between addition and subtraction.

Rewrite rational expressions.

Work with addition and subtraction equations.

Understand the connections between proportional relationships, lines, and linear equations.

Solve equations and inequalities in one variable.

Solve systems of equations.

Understand properties of multiplication and the relationship between multiplication and division.

Write expressions in equivalent forms to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.
problem_activity: Activity
This activity is parallel to one in the previous lesson, except that students are creating a tape diagram after interpreting an equation rather than interpreting a story. The intention is for students to reason in any way that makes sense to them about the equations and diagrams to figure out the solution to each equation. Do not demonstrate any equation solving procedures yet.
For each equation, monitor for a student who used their diagram to reason about a solution and a student who used the structure of the equation to reason about a solution.
Digital
Launch
Give students 5 minutes of quiet work time followed by a whole-class discussion.
Representation: Develop Language and Symbols.
Display or provide charts with symbols and meanings. For example, display a blank template of a tape diagram labeling the different parts with generalizations for what content will go inside. In addition, consider using a previous example situation or equation to make connections to the blank template.
Supports accessibility for: Conceptual processing; Memory
Speaking, Representing: MLR1 Stronger and Clearer Each Time.
Use this routine to give students a structured opportunity to refine their tape diagrams. Ask students to meet with 2–3 partners to get feedback on their diagram of one or both equations. Listeners should press for details from the equations (e.g., “Where is the ___ from the equation in your diagram?”). This will help students use language to describe connections between the diagrams and the equations.
Design Principle(s): Support sense-making
Student Facing
Draw a tape diagram to match each equation.
\(114 = 3x + 18\)
\(114 = 3(y + 18)\)
Use any method to find values for
\(x\)
and
\(y\)
that make the equations true.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Print
Launch
Give students 5 minutes of quiet work time followed by a whole-class discussion.
Representation: Develop Language and Symbols.
Display or provide charts with symbols and meanings. For example, display a blank template of a tape diagram labeling the different parts with generalizations for what content will go inside. In addition, consider using a previous example situation or equation to make connections to the blank template.
Supports accessibility for: Conceptual processing; Memory
Speaking, Representing: MLR1 Stronger and Clearer Each Time.
Use this routine to give students a structured opportunity to refine their tape diagrams. Ask students to meet with 2–3 partners to get feedback on their diagram of one or both equations. Listeners should press for details from the equations (e.g., “Where is the ___ from the equation in your diagram?”). This will help students use language to describe connections between the diagrams and the equations.
Design Principle(s): Support sense-making
Student Facing
\(114 = 3x + 18\)
\(114 = 3(y + 18)\)
Draw a tape diagram to match each equation.
Use any method to find values for
\(x\)
and
\(y\)
that make the equations true.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
To make a Koch snowflake:
Start with an equilateral triangle that has side lengths of 1. This is step 1.
Replace the middle third of each line segment with a small equilateral triangle with the middle third of the segment forming the base. This is step 2.
Do the same to each of the line segments. This is step 3.
Keep repeating this process.
[IMG]
What is the perimeter after step 2? Step 3?
What happens to the perimeter, or the length of line traced along the outside of the figure, as the process continues?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
For each equation, select a student who used their diagram to reason about a solution and a student who used the structure of the equation to reason about a solution. Ask these students to explain how they arrived at a solution. Display the diagram and the equation side by side as students are explaining, and draw connections between the two representations.
Do not demonstrate any equation-solving procedures yet.


correct_option_index: 18